Comprehensive performance analysis of popular odd-symmetric phase masks used for wave-front coded imaging system

(973 Program）No.2009CB724006.

Optimized logarithmic phase masks used to generate defocus invariant modulation transfer function for wavefront coding system

In a previous Letter [Opt. Lett. 33, 1171 (2008)], we proposed an improved logarithmic phase mask by making modifications to the original one designed by Sherif. However, further studies in another paper [Appl. Opt. 49, 229 (2010)] show that even when the Sherif mask and the improved one are optimized, their corresponding defocused modulation transfer functions (MTFs) are still not stable with respect to focus errors. So, by further modifying their phase profiles, we design another two logarithmic phase masks that exhibit more stable defocused MTF. However, with the defocus-induced phase effect considered, we find that the performance of the two masks proposed in this Letter is better than the Sherif mask, but worse than our previously proposed phase mask, according to the Hilbert space angle. (C) 2010 Optical Society of America

Approximate analytical optical transfer function for a wavefront-coded imaging system with two-dimensional rectangularly separable phase masks

Wavefront coding can be used to extend the depth of field of incoherent imaging systems and is a powerful system-level technique. In order to assess the performance of a wavefront-coded imaging system, defocused optical transfer function (OTF) is the metric frequently used. Unfortunately, to the best of our knowledge, among all types of phase masks, it is usually difficult to obtain the analytical OTF except the cubic one. Although numerical computation seems good enough for performance evaluation, the approximate analytical OTF is still indispensable because it can reflect the relationship between mask parameters and system frequency response in a clearer way. Thus, a method is proposed to derive the approximate analytical OTF for two-dimensional rectangularly separable phase masks. The analytical results are well consistent with the direct numerical computations, but the proposed method can be accepted only from engineering point of view and needs rigorous proof in future. (c) 2010 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3485759]

Surface roughness reduction and diffraction efficiency optimisation for e-beam written phase masks

We report the control of surface relief grating parameters and roughness for phase masks produced using e-beam lithography (EBL) and reactive ion etching (RIE). The relationships between processing conditions, grating parameters, surface roughness and the diffraction efficiency of the zeroth and the two first order transmitted beams are discussed.

Surface roughness reduction and diffraction efficiency optimisation for e-beam written phase masks

We report the control of surface relief grating parameters and roughness for phase masks produced using e-beam lithography (EBL) and reactive ion etching (RIE). The relationships between processing conditions, grating parameters, surface roughness and the diffraction efficiency of the zeroth and the two first order transmitted beams are discussed.

Femtosecond laser inscribed phase masks for fibre Bragg grating sensor inscription

We present femtosecond laser inscribed phase masks for the inscription of Bragg gratings in optical fibres. The principal advantage is the flexibility afforded by the femtosecond laser inscription, where sub-surface structures define the phase mask period and mask properties. The masks are used to produce fibre Bragg gratings having different orders according to the phase mask period. The work demonstrates the incredible flexibility of femtosecond lasers for the rapid prototyping of complex and reproducible mask structures. We also consider three-beam interference effects, a consequence of the zeroth-order component present in addition to higher-order diffraction components. © 2012 SPIE.

Optimized phase pupil masks for extended depths of field

By properly designing a phase pupil mask to modulate or encode the optical images and then digitally restoring them, one can greatly extend the depth of field and improve image quality. The original works done by Dowski and Cathey introduce the use of a cubic phase pupil mask to extend the depth of field. The theoretical and experimental researches all verified its effectiveness. In this paper, we suggest the use of an exponential phase pupil mask to extend the depth of field. This phase mask has two variable parameters for designing to control the shape of the mask so as to modulate the wave-front more flexible. We employ an optimization procedure based on the Fisher information metric to obtain the optimum values of the parameters for the exponential and the cubic masks, respectively. A series of performance comparisons between these two optimized phase masks in extending the depth of field are then done. The results show that the exponential phase mask provide slight advantage to the cubic one in several aspects. (c) 2006 Elsevier B.V. All rights reserved.

The Riesz transform and simultaneous representations of phase, energy and orientation in spatial vision

To represent the local orientation and energy of a 1-D image signal, many models of early visual processing employ bandpass quadrature filters, formed by combining the original signal with its Hilbert transform. However, representations capable of estimating an image signal's 2-D phase have been largely ignored. Here, we consider 2-D phase representations using a method based upon the Riesz transform. For spatial images there exist two Riesz transformed signals and one original signal from which orientation, phase and energy may be represented as a vector in 3-D signal space. We show that these image properties may be represented by a Singular Value Decomposition (SVD) of the higher-order derivatives of the original and the Riesz transformed signals. We further show that the expected responses of even and odd symmetric filters from the Riesz transform may be represented by a single signal autocorrelation function, which is beneficial in simplifying Bayesian computations for spatial orientation. Importantly, the Riesz transform allows one to weight linearly across orientation using both symmetric and asymmetric filters to account for some perceptual phase distortions observed in image signals - notably one's perception of edge structure within plaid patterns whose component gratings are either equal or unequal in contrast. Finally, exploiting the benefits that arise from the Riesz definition of local energy as a scalar quantity, we demonstrate the utility of Riesz signal representations in estimating the spatial orientation of second-order image signals. We conclude that the Riesz transform may be employed as a general tool for 2-D visual pattern recognition by its virtue of representing phase, orientation and energy as orthogonal signal quantities.

Eigen-Adaptation and Distributed Representation of 2-D Phase, Energy, Scale and Orientation in Spatial Vision

Distributed representations (DR) of cortical channels are pervasive in models of spatio-temporal vision. A central idea that underpins current innovations of DR stems from the extension of 1-D phase into 2-D images. Neurophysiological evidence, however, provides tenuous support for a quadrature representation in the visual cortex, since even phase visual units are associated with broader orientation tuning than odd phase visual units (J.Neurophys.,88,455–463, 2002). We demonstrate that the application of the steering theorems to a 2-D definition of phase afforded by the Riesz Transform (IEEE Trans. Sig. Proc., 49, 3136–3144), to include a Scale Transform, allows one to smoothly interpolate across 2-D phase and pass from circularly symmetric to orientation tuned visual units, and from more narrowly tuned odd symmetric units to even ones. Steering across 2-D phase and scale can be orthogonalized via a linearizing transformation. Using the tiltafter effect as an example, we argue that effects of visual adaptation can be better explained by via an orthogonal rather than channel specific representation of visual units. This is because of the ability to explicitly account for isotropic and cross-orientation adaptation effect from the orthogonal representation from which both direct and indirect tilt after-effects can be explained.

Perception of surface brightness

The human visual system has adapted to function in different lighting environments and responds to contrast instead of the amount of light as such. On the one hand, this ensures constancy of perception, for example, white paper looks white both in bright sunlight and in dim moonlight, because contrast is invariant to changes in overall light level. On the other hand, the brightness of the surfaces has to be reconstructed from the contrast signal because no signal from surfaces as such is conveyed to the visual cortex. In the visual cortex, the visual image is decomposed to local features by spatial filters that are selective for spatial frequency, orientation, and phase. Currently it is not known, however, how these features are subsequently integrated to form objects and object surfaces. In this thesis the integration mechanisms of achromatic surfaces were studied by psychophysically measuring the spatial frequency and orientation tuning of brightness perception. In addition, the effect of textures on the spread of brightness and the effect of phase of the inducing stimulus on brightness were measured. The novel findings of the thesis are that (1) a narrow spatial frequency band, independent of stimulus size and complexity, mediates brightness information (2) figure-ground brightness illusions are narrowly tuned for orientation (3) texture borders, without any luminance difference, are able to block the spread of brightness, and (4) edges and even- and odd-symmetric Gabors have a similar antagonistic effect on brightness. The narrow spatial frequency tuning suggests that only a subpopulation of neurons in V1 is involved in brightness perception. The independence of stimulus size and complexity indicates that the narrow tuning reflects hard-wired processing in the visual system. Further, it seems that figure-ground segregation and mechanisms integrating contrast polarities are closely related to the low level mechanisms of brightness perception. In conclusion, the results of the thesis suggest that a subpopulation of neurons in visual cortex selectively integrates information from different contrast polarities to reconstruct surface brightness.

Optimized sinusoidal phase mask to extend the depth of field of an incoherent imaging system

Wavefront coding is a powerful technique that can be used to extend the depth of field of an incoherent imaging system. By adding a suitable phase mask to the aperture plane, the optical transfer function of a conventional imaging system can be made defocus invariant. Since 1995, when a cubic phase mask was first suggested, many kinds of phase masks have been proposed to achieve the goal of depth extension. In this Letter, a phase mask based on sinusoidal function is designed to enrich the family of phase masks. Numerical evaluation demonstrates that the proposed mask is not only less sensitive to focus errors than cubic, exponential, and modified logarithmic masks are, but it also has a smaller point-spread-function shifting effect. (C) 2010 Optical Society of America

Cubic sinusoidal phase mask: Another choice to extend the depth of field of incoherent imaging system

Wave-front coding is a well known technique used to extend the depth of field of incoherent imaging system. The core of this technique lies in the design of suitable phase masks, among which the most important one is the cubic phase mask suggested by Dowski and Cathey (1995) [1]. In this paper, we propose a new type called cubic sinusoidal phase mask which is generated by combing the cubic one and another component having the sinusoidal form. Numerical evaluations and real experimental results demonstrate that the composite phase mask is superior to the original cubic phase mask with parameters optimized and provides another choice to achieve the goal of depth extension. (C) 2009 Elsevier Ltd. All rights reserved.